Difference between revisions of "Analytic sheaf"
From Encyclopedia of Mathematics
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| + | $#C+1 = 13 : ~/encyclopedia/old_files/data/A012/A.0102420 Analytic sheaf | ||
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| − | + | A sheaf $ F $ | |
| − | + | on an analytic space $ X $ | |
| − | + | such that for any point $ x \in X $ | |
| + | the set $ F _ {x} $ | ||
| + | is a [[Module|module]] over the ring $ {\mathcal O} _ {x} $ | ||
| + | of germs of holomorphic functions at the point $ x $, | ||
| + | and such that the mapping $ (f , \alpha ) \rightarrow f \alpha $, | ||
| + | defined on the set of pairs $ ( f, \alpha ) $ | ||
| + | where $ f \in {\mathcal O} _ {x} $, | ||
| + | $ \alpha \in F _ {x} $, | ||
| + | is a continuous mapping of $ {\mathcal O} \times F $ | ||
| + | into $ F $ | ||
| + | for $ x \in X $. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H. Grauert, R. Remmert, "Theory of Stein spaces" , Springer (1979) (Translated from German)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H. Grauert, R. Remmert, "Coherent analytic sheaves" , Springer (1984) (Translated from German)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H. Grauert, R. Remmert, "Theory of Stein spaces" , Springer (1979) (Translated from German)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H. Grauert, R. Remmert, "Coherent analytic sheaves" , Springer (1984) (Translated from German)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 07:54, 16 April 2023
A sheaf $ F $
on an analytic space $ X $
such that for any point $ x \in X $
the set $ F _ {x} $
is a module over the ring $ {\mathcal O} _ {x} $
of germs of holomorphic functions at the point $ x $,
and such that the mapping $ (f , \alpha ) \rightarrow f \alpha $,
defined on the set of pairs $ ( f, \alpha ) $
where $ f \in {\mathcal O} _ {x} $,
$ \alpha \in F _ {x} $,
is a continuous mapping of $ {\mathcal O} \times F $
into $ F $
for $ x \in X $.
References
| [a1] | H. Grauert, R. Remmert, "Theory of Stein spaces" , Springer (1979) (Translated from German) |
| [a2] | H. Grauert, R. Remmert, "Coherent analytic sheaves" , Springer (1984) (Translated from German) |
How to Cite This Entry:
Analytic sheaf. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Analytic_sheaf&oldid=18711
Analytic sheaf. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Analytic_sheaf&oldid=18711
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article